Internal problem ID [3184]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 439.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x -y\right ) y^{\prime }-\left (2 y x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((x-y(x))*diff(y(x),x) = (1+2*x*y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{\operatorname {LambertW}\left (-{\mathrm e}^{x^{2}} c_{1} x \right )} \]
✓ Solution by Mathematica
Time used: 5.233 (sec). Leaf size: 29
DSolve[(x-y[x])y'[x]==(1+2 x y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{W\left (x \left (-e^{x^2-c_1}\right )\right )} \\ y(x)\to 0 \\ \end{align*}